Generalization of the Theory of Transition Times in Metabolic Pathways: A Geometrical Approach

Lloréns, Mónica; Nuño, Juan Carlos; Rodrı́guez, Yoel; Meléndez-Hevia, Enrique; Montero, Francisco

doi:10.1016/s0006-3495(99)76869-4

Cited by 40 publications

(46 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Previously, quantitative computational simulation proved to support understanding of regulatory systems [5][6][7][8][9][10] , characterizing threshold properties and bistability 11,12 , characteristic times 13,14 and feedback effects 12,[15][16][17][18][19] . The model presented here comprises receptor stimulation, the HOG signaling pathway, activation of gene expression, adaptation of cellular metabolism, glycerol accumulation and a thermodynamic description of the control of volume and osmotic pressure.…”

mentioning

confidence: 99%

Integrative model of the response of yeast to osmotic shock

et al. 2005

View full text Add to dashboard Cite

Integration of experimental studies with mathematical modeling allows insight into systems properties, prediction of perturbation effects and generation of hypotheses for further research. We present a comprehensive mathematical description of the cellular response of yeast to hyperosmotic shock. The model integrates a biochemical reaction network comprising receptor stimulation, mitogen-activated protein kinase cascade dynamics, activation of gene expression and adaptation of cellular metabolism with a thermodynamic description of volume regulation and osmotic pressure. Simulations agree well with experimental results obtained under different stress conditions or with specific mutants. The model is predictive since it suggests previously unrecognized features of the system with respect to osmolyte accumulation and feedback control, as confirmed with experiments. The mathematical description presented is a valuable tool for future studies on osmoregulation in yeast and-with appropriate modifications-other organisms. It also serves as a starting point for a comprehensive description of cellular signaling.Osmoregulation encompasses active processes with which cells monitor and adjust osmotic pressure and control shape, turgor and relative water content. Even individual cells in multicellular organisms respond to osmotic changes, and strategies of cellular adaptation are conserved from bacteria to human 1 . The yeast Saccharomyces cerevisiae is a suitable model system to study osmoregulation and a substantial amount of information is available on osmotic shockinduced signal transduction, control of gene expression and accumulation of osmolytes 2 .Osmoregulation is a homeostatic process, though commonly studied as a response to osmotic shock. Central to yeast osmotic adaptation is the high osmolarity glycerol (HOG) signaling system 2,3 (Fig. 1). S. cerevisiae monitors osmotic changes through the plasma membrane-localized sensor histidine kinase Sln1. Under ambient conditions, Sln1 is active and inhibits signaling. Upon loss of turgor pressure, Sln1 is inactivated 4 resulting in activation of a mitogen-activated protein (MAP) kinase cascade and phosphorylation of the MAP kinase Hog1. Active Hog1 accumulates in the nucleus where it affects gene expression. Two HOG target genes encode enzymes in glycerol production. Hence, activation of Hog1 stimulates the production of glycerol, which serves as an osmolyte to increase intracellular osmotic pressure. Glycerol accumulation is also controlled by rapid closing of the aquaglyceroporin Fps1, which is an osmolarity-regulated glycerol channel. Hog1 activation and Hog1-dependent transcriptional stimulation are transient processes, indicating rigorous feedback control. Several protein phosphatases are known as negative regulators of the pathway. Although the overall organization of the systems is well characterized, open questions concern the mechanisms underlying activation and deactivation of the system, feedback control and the causal relationship between different events in...

show abstract

mentioning

confidence: 99%

Integrative model of the response of yeast to osmotic shock

et al. 2005

View full text Add to dashboard Cite

show abstract

“…For a complete explanation of the meaning of T c see Llorens et al (1999). According with this definition the characteristic time provides an average time to reach the equilibrium state from any initial condition along the trajectory.…”

Section: Characteristic Time For a Simple Replicator Systemmentioning

confidence: 99%

“…The stop control was set to keep the difference between successive steps of variable I 2 at less than 10 À4 during 200 steps. The characteristic time was then calculated, as described in Llorens et al (1999), by computing the quotient between the area, computed by the classical trapezoid rule, over the trajectory of I 2 and below the horizontal asymptote that corresponds to its stationary value and the height of this asymptote. Fig.…”

Section: A Two Peak Separated By a Neutral Valley Fitness Landscapementioning

confidence: 99%

“…The characteristic time, hereafter referred to as T c (Llorens et al, 1999), was previously defined to capture the global evolutionary properties of dynamical systems. Based on a geometrical interpretation, the characteristic time provides the average time the system takes to change from one state to another under the action of a perturbation or a persistent variation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Characteristic time in quasispecies evolution

Marín

Tejero

Nuño

et al. 2012

Journal of Theoretical Biology

Self Cite

View full text Add to dashboard Cite

a b s t r a c tThe time a phenotype takes to achieve a stationary state from an initial condition depends on multiple factors. In particular, it is a function of both its fitness and its mutation rate. We evaluate the average time, referred to as the characteristic time, T c , that the system takes to reach a final steady state of simple models of populations formed by self-replicative sequences. The dependence of T c on the mutation rate and on the fitness landscape is also studied. For simple fitness landscapes, e.g. single peak, the characteristic time can be analytically obtained as a function of the system parameters. In this case, T c for obtaining the quasispecies distribution presents a maximum at a Q-value that depends on the initial conditions and decreases monotonously as the mutation rate tends to zero. For most of the complex landscapes handled in this paper, the characteristic time to achieve the quasispecies distribution picked around the fittest phenotype attains a local minimum for a given mutation rate between 0 and the Q-value at which T c reaches its local maximum. Thus, in these cases, an optimum value for the mutation rate exists that corresponds to the lowest value of the characteristic time for quasispecies evolution.

show abstract

“…A change in the concentration thus varies the ratios of the relaxation times. Unfortunately, the estimation of characteristic times is exceedingly difficult if no analytical expressions are known [49]. A more detailed description of feedback loops can change the dynamic behavior of the system and its characteristic parameters in comparison to a quasi-stationary approximation, whereas the steady state is unchanged.…”

Section: Quasi-stationary States In Feedback Mechanismsmentioning

confidence: 99%

Approximations and their consequences for dynamic modelling of signal transduction pathways

Millat

Bullinger

Rohwer

et al. 2007

Mathematical Biosciences

View full text Add to dashboard Cite

This version is available at https://strathprints.strath.ac.uk/11996/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system and its approximations with respect to the transient and steady state behavior. Approximations and their Consequences for Dynamic Modelling of Signal Transduction Pathways

show abstract

Generalization of the Theory of Transition Times in Metabolic Pathways: A Geometrical Approach

Cited by 40 publications

References 28 publications

Integrative model of the response of yeast to osmotic shock

Integrative model of the response of yeast to osmotic shock

Characteristic time in quasispecies evolution

Approximations and their consequences for dynamic modelling of signal transduction pathways

Contact Info

Product

Resources

About